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A diner asks patrons for their preference for waffles or pancakes and syrup or fruit topping.

The table shows the probabilities of results.

A diner asks patrons for their preference for waffles or pancakes and syrup or fruit topping The table shows the probabilities of results class=

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Answer:

[tex]P (Waffles | Syrup)\neq P(Waffles)[/tex]

Step-by-step explanation:

From the table we have to:

Probability of syrup is 0.96

Probability of waffles and syrup is 0.32

P (Waffles | Syrup) = P (Waffles and syrup) / P (syrup)

So:

If this equality is met, the probabilities are dependent, if on the contrary

P (Wafles | Syrup) = P (Wafles) then are independent probabilities.

[tex]P (Wafles | Syrup) = 0.32 / 0.96 = 0.333 \neq 0.32[/tex]

So we have to:

[tex]P (Waffles | Syrup)\neq P(Waffles)[/tex]

The probabilities are dependent.

Answer:

Preference for waffies and syrup are dependent events and

[tex]P(waffies\mid syrup)\neq P(waffies)[/tex]

Step-by-step explanation:

Since we have given that

[tex]P(waffies)=0.34[/tex]

[tex]P(syrup\cap waffies)=0.32[/tex]

As we know that if A and B are independent it must satisfy ,

[tex]PA\cap B)=P(A).P(B)[/tex]

But here,

[tex]P(waffies\cap syrup)\neq P(waffies).P(syrup)\\0.32\neq 0.34\times 0.96\\0.32\neq 0.3264[/tex]

Hence, they are not independent i.e. they are dependent.

And

[tex]P(waffies\mid syrup)\neq P(waffies)[/tex]

Because,

[tex]P(waffies\mid syrup)\\\\=\frac{P(waffies\cap syrup)}{P(syrup)}\\\\=\frac{0.32}{0.96}\\\\=0.33[/tex]

but,

[tex]P(waffies)=0.34[/tex]


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